Power MOSFETs (Metal Oxide Semiconductor Field Effect Transistors) are used as switching elements in e.g. portable terminal equipment such as mobile phones and mobile personal computers. In the power MOSFET, for lower power consumption, reduction of on-resistance of the channel layer is required. For instance, by thinning the gate insulating film, population inversion is enhanced to increase the carrier density of the channel layer. This is a conventional method for reducing the on-resistance of the channel layer. However, if the on-resistance reduction is enhanced by this method, the leakage current increases due to the tunnel current of the gate insulating film. Thus, to enhance population inversion even for a thick gate insulating film, it has been investigated to use a dielectric film with high dielectric constant for the gate insulating film.